A dynamical approach to compactify the three dimensional Lorentz group

摘要

The Lorentz group acts on the projectivized light cone in the three dimensional Lorentz space as the group G of Mobius transformations of the circle. We find the closure of G in the space of all measurable functions of the circle into itself, obtaining a compactification. of it as an open dense subset of the three-sphere, with a dynamical meaning related to generalized flows.